document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=69849>Question 69849</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534494498/algebrahomeworkh>Algebra & Trigonometry with Geometry</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Help! Submitted these problems on Monday of thsi week and haven't receieved a response. Please help studying for final exam.\r<BR>\n" );
document.write( "\n" );
document.write( "For the function defined by f(x)=5x-5, find a formula for f-^1(x).\r<BR>\n" );
document.write( "\n" );
document.write( "Solve the equation 4^2x+1=2^3x+6.\r<BR>\n" );
document.write( "\n" );
document.write( "Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=2, that passes through the point P(1,4).\r<BR>\n" );
document.write( "\n" );
document.write( "A bacteria culture started with a count of 480 at 8:00 a.m. and after t hours is expected to grow to f(t)=480(3/2)t. Estimate the number of bacteria in the culture at noon the same day.\r<BR>\n" );
document.write( "\n" );
document.write( "If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate of 6% per year, then its value t years after the purchase will be f(t)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years 2005 and 2008?\r<BR>\n" );
document.write( "\n" );
document.write( "For the function defined by f(x)=2-x^2, 0 < x, use a sketch to help find a formula for f-^1(x).\r<BR>\n" );
document.write( "\n" );
document.write( "The amount of a radioactive tracer remaining after t days is given by A=Ao e^-0.058t, where Ao is the starting amount at the beginning of the time period. How many days will it take for one half of the original amount to decay?\r<BR>\n" );
document.write( "\n" );
document.write( "Thanks everyone for helping me out. God Bless, John\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49770 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=49770\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the function defined by f(x)=5x-5, find a formula for f-^1(x<BR>\n" );
document.write( "y=5x-5<BR>\n" );
document.write( "Interchange x and y to get:<BR>\n" );
document.write( "x=5y-5<BR>\n" );
document.write( "Solve for y:<BR>\n" );
document.write( "y=(1/5)x+1<BR>\n" );
document.write( "That is f^-1<BR>\n" );
document.write( "-------------------\r<BR>\n" );
document.write( "\n" );
document.write( "Solve the equation 4^2x+1=2^3x+6.<BR>\n" );
document.write( "Is that 16x+1=8x+6  ?<BR>\n" );
document.write( "or is it<BR>\n" );
document.write( "4^(2x)+1 = 2^(3x)+6 ?<BR>\n" );
document.write( "???<BR>\n" );
document.write( "-------------------------- <BR>\n" );
document.write( "Find an exponential function of the form f(x)=ba^x+c with y-intercept 2, horizontal asymptote y=2, that passes through the point P(1,4).<BR>\n" );
document.write( "Form: y=ab^x+c<BR>\n" );
document.write( "If y-intercept=2 then y=a+2<BR>\n" );
document.write( "If horizontal asymptote is y=2 then c=2<BR>\n" );
document.write( "If Passes through point (1,4) then 4=ab+2; ab=2<BR>\n" );
document.write( "EQUATION: y=2^x + 2<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "A bacteria culture started with a count of 480 at 8:00 a.m. and after t hours is expected to grow to f(t)=480(3/2)t. Estimate the number of bacteria in the culture at noon the same day.\r<BR>\n" );
document.write( "\n" );
document.write( "8 to noon is 4 hour<BR>\n" );
document.write( "Let t=4 in your equation<BR>\n" );
document.write( "f(4)=480(3/2)^4<BR>\n" );
document.write( "f(4)=2430<BR>\n" );
document.write( "------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate of 6% per year, then its value t years after the purchase will be f(t)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years 2005 and 2008?<BR>\n" );
document.write( "In 1998 you have the value; that is when t=0<BR>\n" );
document.write( "In 2005 t=2005-1998=7; find f(7)<BR>\n" );
document.write( "In 2008 t=2008-1998=10; find f(10)<BR>\n" );
document.write( "Subtract f(7) from f(10) to get the increase over that period.<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( " <BR>\n" );
document.write( "For the function defined by f(x)=2-x^2, 0 < x, use a sketch to help find a formula for f-^1(x). <BR>\n" );
document.write( "Sketch or graph the given function.<BR>\n" );
document.write( "Draw the line y=x on the same coordinate system<BR>\n" );
document.write( "Sketch the curve symetric to the given curve relative to the line y=x.<BR>\n" );
document.write( "For example if you have the point (0,1) in the 1st curve you want the<BR>\n" );
document.write( "point (1,0) in the inverse function curve.  What you are doing is really<BR>\n" );
document.write( "interchange x and y in all the points.\r<BR>\n" );
document.write( "\n" );
document.write( "That is the curve of f^-1(x)<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "The amount of a radioactive tracer remaining after t days is given by A=Ao e^-0.058t, where Ao is the starting amount at the beginning of the time period. How many days will it take for one half of the original amount to decay?<BR>\n" );
document.write( "You want A=(1/2)Ao<BR>\n" );
document.write( "You get:<BR>\n" );
document.write( "(1/2)Ao=Aoe^(-0.58t)<BR>\n" );
document.write( "1/2=e^(-0.58t)<BR>\n" );
document.write( "Take the natural log to get:<BR>\n" );
document.write( "ln(1/2) = -0.58t<BR>\n" );
document.write( "Solve for t.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );